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Large-eddy simulation of pulverized coal combustion using flamelet model
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Large-eddy simulation of pulverized coal combustion using flamelet model Junya Watanabe a,∗, Teruyuki Okazaki a, Kenji Yamamoto a, Koji Kuramashi b, Akira Baba b a Research
& Development Center, Mitsubishi Hitachi Power Systems, Ltd., 832-2 Horiguchi, Hitachinaka-shi, Ibaraki-ken 312-0034, Japan b Boiler Products Headquarters, Mitsubishi Hitachi Power Systems, Ltd., Japan Received 4 December 2015; accepted 5 June 2016 Available online xxx
Abstract A flamelet model for pulverized coal combustion, which considers three mixture fractions for coal moisture, volatile matter and gasified char, has been coupled with a large-eddy simulation. Its prediction accuracy for ignition and extinction has been investigated in the configurations of a lab-scale coal jet flame and a large-scale test furnace with an actual coal burner. For the lab-scale coal jet flame, the profile of the ratio of coal burnt on the central axis of the coal jet was compared with the measurement. The profile by the flamelet model well agreed with the experimental data within the measurement error. For the large-scale test furnace with the actual burner, the prediction ability for the ignition limit in a decreasing coal feed rate was examined. The present simulation reproduced an unstable flame state occurring at a lower coal feed rate. The ignition stability index, which was evaluated from the flame images, was compared with the test result. The sharp decline of the ignition stability index near the ignition limit was well-captured by the present simulation. The prediction error for the coal feed rate at the ignition limit was estimated to be within 10%. © 2016 by The Combustion Institute. Published by Elsevier Inc. Keywords: Pulverized coal combustion; Flamelet model; Large-eddy simulation; Turbulent jet flame; Ignition
1. Introduction We have to improve the pulverized coal combustion technologies to attain highly-efficient combustion and lower NOx emission in coal-fired thermal power plants. To develop innovative combustion
∗
Corresponding author. E-mail address: [email protected] (J. Watanabe).
technologies, the combustion state inside a coalfired boiler must be understood in detail. However, the huge size of boiler restricts thorough combustion tests in a real-scale. Also, quantitative measurements of pulverized coal combustion field are difficult. Numerical analysis is a powerful tool for a deep understanding of the phenomena and simulations of pulverized coal combustion have been extensively conducted. Recently, large-eddy simulation (LES) of pulverized coal combustion has been applied to laboratory-scale burners [1–5]. In our
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group, LES was also applied to a large-scale boiler furnace with a coal feed rate of 3000 kg/h [6]. The choice of turbulent combustion model affects the prediction accuracy of the simulation. In previous simulations of pulverized coal combustion, the eddy-breakup model and eddy dissipation model [7] have often been used because of their extensive application range. However, the concept of these models is intuitive as both unreasonably replace the chemical reaction time scale with a turbulent time scale [8]. These models also do not consider the flame structure that interacts with turbulence. Thus, these models cannot correctly reflect the influence of chemical kinetics and turbulence-chemistry interactions. In order to reproduce such non-equilibrium behavior as ignition and extinction, more sophisticated models that consider the finite rate chemistry with a detailed reaction mechanism are preferred. The high computational cost of such models for practical use is not affordable, however. The flamelet model is promising because it can take detailed chemical kinetics into account at a reasonable computational cost. Various flamelet models have been developed and applied to simulations of gaseous combustion [9–14] and spray combustion [15–17]. However, no flamelet model had been coupled with a coal combustion model that takes both devolatilization and the char surface reaction into account, although a flamelet model applied to gasified coal volatile combustion has been reported [18,19]. We proposed a new flamelet model concept applicable to the simulation of pulverized coal combustion in our previous study [20]. In the present study, the flamelet model is coupled with the LES to simulate a real combustor. The objective is to accurately reproduce the ignition of a pulverized coal burner, which is an important phenomenon for the combustor performance. The prediction accuracy for coal particle ignition and extinction is investigated in the configurations of a lab-scale coal jet flame and a large-scale test furnace with an actual burner.
Prandtl number is constant at 0.8. The radiation source term in the enthalpy equation is calculated by a discrete transfer radiation method [3,22]. The governing equations are solved by a finite volume method. The PISO approach [23] is employed to solve pressure–velocity coupling. The time step is determined so that the maximum Courant number is less than 0.2. A second order central difference scheme is used to calculate the convection terms. The minmod limiter function is applied for scalar equations. The diffusion term is evaluated by a second order central difference scheme. The mass, momentum and energy equations for coal particles are the same as those in [3] except that the moisture in coal particles is taken into account in the mass conservation equation.
2. Numerical methods
where ρ is the gas density, ui is the gas velocity, α is the thermal diffusivity, α sgs is the SGS thermal diffusivity, mmoi is the mass of moisture in a coal particle, mvol is the mass of volatile matter, mchar is the mass of char, and Vcell is the volume of a mesh cell. Overbar and tilde signs denote the spatial averaging and Favre averaging, respectively. The particlein-cell model [24] is used to calculate the last terms in Eqs. (1)–(3) [6]. The Lewis number is assumed to be unity. Here, Zmoi , Zvol and Zchar are defined as:
2.1. Governing equations The gas phase and coal particles are solved in an Eulerian manner and a Lagrangian manner, respectively. The Favre-filtered conservation equations for mass, momentum, enthalpy, and the state equation for ideal gas are solved in the gas phase. The source terms due to coal combustion are taken into account for the mass, momentum, and enthalpy conservation equations [3]. The subgrid-scale (SGS) stress tensor in the momentum equation is calculated by the Smagorinsky model [21]. The SGS thermal diffusivity in the enthalpy equation is calculated by assuming that the SGS turbulent
2.2. Flamelet model for coal combustion We extend the flamelet model for coal combustion developed in our previous study [20] to consider the moisture in a coal particle. In this model, the following Favre-filtered transport equations are solved: ∂ ρ¯ Z˜ moi ∂ ρ¯ u˜i Z˜ moi ∂ ∂ Z˜ moi + = ρ( ¯ α + α sgs ) ∂t ∂ xi ∂ xi ∂ xi 1 dmmoi − , Vcell parcel dt ∂ ρ¯ Z˜ vol ∂ ρ¯ u˜i Z˜ vol ∂ ∂ Z˜ vol + = ρ( ¯ α + α sgs ) ∂t ∂ xi ∂ xi ∂ xi 1 dmvol − , Vcell parcel dt ∂ ρ¯ Z˜ char ∂ ρ¯ u˜i Z˜ char ∂ ∂ Z˜ char + = ρ( ¯ α + α sgs ) ∂t ∂ xi ∂ xi ∂ xi 1 dmchar − , Vcell parcel dt
Z˜ moi = Z˜ vol =
Please cite this article as: J. Watanabe et al., coal combustion using flamelet model, Proceedings http://dx.doi.org/10.1016/j.proci.2016.06.031
(1)
(2)
(3)
m moi , m moi + m vol + m char + m ox
(4)
m vol , vol + m char + m ox
(5)
m
moi
+
m
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Z˜ char
m char = m moi + m vol + m char + m ox
where mmoi
(6)
evaporating moisture, mvol
is the mass of is the mass of gas originating from the volatile matter, mchar is the mass of gas originating from the char and mox is the mass of gas originating from the oxidant. The present model is based on the flamelet/progress variable (FPV) approach [10]. The following conservation equation of the progress variable Cpv is solved: ∂ C˜ pv ∂ ρ¯C˜ pv ∂ ρ¯ u˜iC˜ pv ∂ + = ρ¯ α + αsgs + S¯C pv ∂t ∂ xi ∂ xi ∂ xi (7) where SCpv is the source term of Cpv . In this study, we use the CO2 mass fraction as the progress variable (Cpv = YCO2 ). 2.3. Flamelet database The database of the species compositions are obtained by solving the flamelet equations. To avoid solving multi-dimensional flamelet equations [25,26], we introduce the following variables: Z˜ = Z˜ vol + Z˜ char + Z˜ moi
Table 1 Coal properties. Proximate analysis (dry basis wt%) Volatile matter Char Ash Fuel composition originating from the volatile matter, Yvol,k × 100 (wt%) CO CH4 C2 H2
Z˜ char m char = , m vol Z˜ vol
(9)
B=
Z˜ vol m vol = . m moi Z˜ moi
(10)
Ordinary one-dimensional flamelet equations with a single scalar dissipation rate χ are solved in Z space at different values of A and B. Depending on the values of A and B, the fuel composition of the flamelet equations changes. The details for determining the fuel composition are described in [20]. The fuel composition is determined as m moi Ymoi,k + m vol Yvol,k + (m char + m ox,conv )Ychar,k m moi + m vol + m char + m ox,conv MO2 +υMN2 1 A Ychar,k B Ymoi,k + Yvol,k + A + 0.5 MC = , (11) MO2 +υMN2 1 A B + 1 + A + 0.5 M
Y f uel,k =
C
where Ymoi,k is the composition of moisture, Yvol,k is the composition of gasified volatile matter, Ychar,k is the composition of gas produced through the char surface reaction, and mox,conv is the mass of oxidant consumed by the following char oxidation reaction: C + 0.5(O2 + υN2 ) → CO + 0.5υN2 .
(12)
MO2 , MN2 and MC denote the molecular weights of O2 , N2 and C, respectively. For the air oxidant, υ
31.1 54.0 14.9 34.8 24.5 40.7
is 3.76. Thus, CO and N2 are contained in the fuel gas from the char. Figure 1 shows the change of fuel composition Yfuel,k as a function of A and B for a bituminous coal having the properties listed in Table 1. The change of fuel composition is large for A < 1 and B < 4. Sufficient numbers of data points should be obtained in these ranges. The upper bound of Z in the flamelet equations, where the fuel composition is imposed, is calculated as Zmax = =
(8)
A=
3
m moi + m vol + m char m moi + m vol + m char + m ox,conv 1 B
1 B
+1+A
+υMN2 + 1 + A + 0.5 MO2M A
.
(13)
C
Also, the temperature assigned for the fuel gas is calculated by considering the temperature increase due to the heat of reaction of Eq. (12). The temperature increase is estimated by T =
Qox A +υMN2 Cp, f uel 1 + A + 0.5 MO2M A
(14)
C
where Qox is the heat of reaction of Eq. (12), and Cp,fuel is the specific heat of the fuel gas. Equation (14) assumes that all the heat released from the reaction (12) is transferred directly to the gas phase. Note that the fuel temperature estimated by using Eq. (14) gives only a reference value. In the present model, the flamelet database is generated at various temperatures decreasing from the reference temperature. This procedure makes it possible to consider the heat loss effect caused by radiation and the heat transfer to the solid phase in the flamelet database. The flamelet database is generated by FlameMaster [27] which solves the steady onedimensional flamelet equations at p = 0.1 MPa without radiation heat loss. The GRI-Mech 3.0 [28] is used as the reaction mechanism. Figure 2 shows the temperature profiles as a function of mixture fraction for different values of A and B. The profiles are for different levels of the progress variable. For B = 0.0, there is no temperature increase because only moisture is contained as the fuel gas. The peak temperature increases at higher
Please cite this article as: J. Watanabe et al., coal combustion using flamelet model, Proceedings http://dx.doi.org/10.1016/j.proci.2016.06.031
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Mass fraction of fuel Yfuel,k
4
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(a) B = 4.0 CH4 CO H2O
1 0.8
C2H2 N2
0.6 0.4 0.2
0 0
1
2
3
4
5
Mass fraction of fuel Yfuel,k
A 1
(b) A = 0.5
CH4 CO H2O
0.8
C2H2 N2
0.6 0.4 0.2 0 0
2
4
6
8
10
B Fig. 1. Fuel composition in flamelet equations as a function of (a) A at B = 4.0, and (b) B at A = 0.5.
Fig. 2. Temperature profiles as a function of Z for different A and B values. Arrows pointing to increasing Cpv are shown in each graph.
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5
Fig. 3. Instantaneous gas temperature distributions in the center plane.
B because less moisture is contained in the fuel gas at higher B. Also, the peak temperature increases at higher A, in which the char combustion progresses. Zmax becomes lower at higher A and B. The enthalpy h, which is obtained from the energy conservation equation including the heat source terms due to radiation and coal combustion, is also used as a reference parameter to take the effect of heat loss into account. As described above, the flamelet data are calculated at various fuel and oxidant temperatures to reproduce various enthalpy states. The fuel composition is determined from the flamelet data with the corresponding enthalpy value. In the present simulation, we couple the flamelet model with the LES. To take the SGS turbulence/chemistry interaction into account, a presumed probability density function (PDF) approach is introduced, in which the filtered quantities are written as ϕ˜ =
Zmax
ϕ (Z )P (Z )dZ.
(15)
0
A beta-PDF [1,29] is used to model the mixture fraction distribution. Consequently, the gas composition is determined from the flamelet database as Y˜ k = Yk Z˜ , Z˜ 2 , C˜ pv , A, B, h˜ . (16) In the present case, the flamelet data points are 100 × 20 × 30 × 5 × 5 × 7 for Z˜ × Z˜ 2 × C˜ pv × A × B × h˜ . The memory size for this database is approximately 1.5GB.
Table 2 Inlet conditions for lab-scale coal jet flame.
Zmoi Zvol Zchar Cpv
Primary jet
Preheated gas
Side boundary
0.01 0.0 0.0 0.0
0.082 0.041 0.0 0.133
0.0 0.0 0.0 0.0
3. Application to a lab-scale coal jet flame 3.1. Numerical conditions First, we apply the present simulation to a labscale ignition experiment, which has the same configuration and conditions as in our previous work [3] and details are given there. The mixture of pulverized coal and air is injected through the center nozzle and ignited by the co-flowing preheated gas. The diameter of the center nozzle is 7 mm. The injection velocity of primary jet is 10 m/s and the velocity of preheated gas is 4.8 m/s. The temperature of the preheated gas is 1510 K. The Reynolds number of the primary jet is about 4500. The case simulated here has the inlet stoichiometric ratio of 0.22. The inlet boundary conditions for the flamelet simulation are listed in Table 2. 3.2. Numerical simulation results Figure 3 shows instantaneous gas temperature distributions in the center plane. The flamelet model results are plotted in Fig. 3(a) and previous results [3] obtained by an eddy-dissipation concept (EDC) model are shown in Fig. 3(b). Qualitatively
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points. It is implied that the flamelet model captures the jet core temperature (shown in Fig. 3) more accurately than the EDC model.
60 Flamelet model EDC model [8] Exp.
50 40 30
4. Application to a large-scale test furnace with an actual pulverized coal burner
20 10
4.1. Experimental and numerical conditions
0 0
100
200 300 400 Axial position, mm
500
Fig. 4. Comparison of the ratio of coal burnt on the centerline.
similar turbulent combustion fields can be observed for both simulations. The turbulent mixing layer develops between the primary jet and the preheated co-flow. A lifted flame is formed there. The flame temperature is almost the same for both simulations, although the relatively low-temperature jet core remains more downstream in the EDC model. Figure 4 compares the distribution of the ratio of coal burnt on the centerline. The simulation results by the flamelet model and the EDC model [3] are compared with the experimental data by the probe sampling [30]. Overall, good agreement with the experiment is obtained for both simulations. In the EDC model, the ratio of coal burnt is underestimated at the position 300 mm downstream from the nozzle exit. On the other hand, in the flamelet model, the ratio of coal burnt starts to increase earlier than in the EDC model and its distribution is within the measurement error at all measurement
Our second application is for a low-load testing of the HT-NR3 burner [31] in a large-scale test rig. Figure 5 shows the computational mesh of the test rig. A single burner is attached on the furnace. The mesh has approximately 840,000 cells and is refined only near the burner because we focus on the ignition state that occurs in the burner zone. The diameter of the primary nozzle exit is 447 mm. To investigate the ignition limit of the burner, the mass flow rate of coal is decreased from a stably combusting state under a constant air flow rate condition. The mass flow rates are 2.62 kg/s for the burner air and 0.56 kg/s for the additional air, respectively. The boundary conditions for Zmoi , Zvol , Zchar and Cpv are fixed to be zero at all inlet boundaries. 4.2. Results of combustion test Figure 6 shows images of the flame taken near the burner in a decreasing coal feed rate. Four arbitrary instants are selected for the images to observe the unsteady behavior. The flame stabilizing ring (FSR) attached at the primary nozzle exit is drawn as a solid line in the images. In all cases, a luminous flame is formed from the FSR. The luminous flame occasionally disappears for a part of
Outlet Additional air ports
Secondary air Primary nozzle
Coal + Primary air
Secondary air
HT-NR3 burner
Furnace
Fig. 5. Computational mesh for large-scale test furnace.
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Coal feed rate
Low
7
High
FSR No.1 A
A No.2
A No.3 A
A No.4 A
Fig. 6. Flame images in the combustion test.
a E D C
FSR A B
Gas temperature [K] 350 1900
b Recirculation region
Ignition region
Unburnt region
Fig. 7. Simulated instantaneous gas temperature distribution (a) in the vertical plane through the center of the burner and (b) on the dashed line “E”.
FSR at lower coal feed rates, as shown by “A” in the images. At the lowest coal feed rate in the test, the flame is highly unstable because partial disappearance of the luminous flame frequently occurs. The coal feed rate decrease is stopped here to avoid the flame extinction. 4.3. Numerical results Figure 7(a) shows the instantaneous gas temperature distribution in the vertical plane through
the center of the burner under a stably combusting state. The primary air with pulverized coal flows straightly (arrow “A”) and the secondary air flows outwardly (arrow “B”). These two flows generate a large recirculation flow (arrow “C”) behind the FSR. A part of the hot burnt gas is entrained by this recirculation flow, enhancing the ignition of pulverized coal near the FSR. The gas temperature rapidly increases just behind the FSR and the stable flame develops downstream (region “D”). Figure 7(b) shows the gas temperature profile on
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Coal feed rate
Low
High
Fig. 8. Simulated isosurfaces of 1400 K in a decreasing coal feed rate.
Fig. 9. Examples to evaluate the ignition stability index. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)
the dashed line “E” shown in Fig. 7(a). The temperature of burnt gas in the recirculation zone is roughly 1260 K. The temperature rapidly increases between the unburnt primary air and the recirculation zone. The coal particles are heated and ignition occurs in this region. The coal jet flame ignited by the burnt gas can be detected by temperature isosurfaces of 1400 K, which is about 10% higher than that of the burnt gas. Figure 8 shows instantaneous isosurfaces of 1400 K. An arbitrary instant is shown. A highly turbulent flame can be observed. At higher coal feed rates, the flame is formed on the entire circumference of the FSR. At the second lowest coal feed rate, the flame region decreases remarkably and it is formed on only a part of the FSR. At the lowest coal feed rate, only a small flame can be observed.
to d is calculated for each image, averaging for Ns -number of images. Figure 10 compares the ignition stability index for lowering coal feed rates between the experiment and the simulation. The coal feed rates are normalized by the value in the stably combusting state. The flame stability index rapidly decreases below the normalized coal feed rate of 0.6 in the combustion experiment. This trend is well reproduced by the present simulation, although the numerical value is slightly lower than the experimental one. When the ignition stability index at the lowest coal feed rate in the experiment is used as a criterion, the error of the coal feed rate at the ignition limit is 9.6% in the present simulation. Thus, the present simulation predicts the ignition limit with less than 10% error.
4.4. Comparison of ignition stability 5. Conclusions To evaluate the ignition stability from the flame images shown in Figs. 6 and 8, we define the following index: Ignition stability index (%) =
Ns 1 l · 100. (17) Ns i=1 d
Figure 9 shows examples to evaluate the ignition stability index. Here, d is the length of the primary nozzle diameter in the flame image. The vertical line with a length of d (shown as a dashed line) is put at the position of d apart from the nozzle exit. Then, the luminous flame area on the vertical line (marked by the short red lines) is manually detected and its length is l. The percentage of l
The LES coupled with the newly-developed flamelet model for pulverized coal combustion was demonstrated in two configurations of a lab-scale coal jet flame and a large-scale combustion test of an actual pulverized coal burner. For the lab-scale coal jet flame, the profile of the ratio of coal burnt obtained by the present flamelet model was compared with the experiment and our previous simulation using an EDC model. The prediction accuracy of the ratio of coal burnt near the ignition point was improved compared to the EDC model. The profile of the ratio of coal burnt obtained by the present simulation was within the measurement error on the central axis.
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9
100 80 Experiment Simulation
60
40 20
Error 9.6%
0 0
0.2 0.4 0.6 0.8 1 1.2 Normalized coal feed rate (arb. unit)
Fig. 10. Comparison of ignition stability index.
For the large-scale combustion test of an actual pulverized coal burner, where the coal feed rate was lowered from a stably combusting state, the present simulation reproduced the unstable flame observed in the test near the ignition limit. The prediction error for the coal feed rate at the ignition limit was estimated to be within 10% in the present case. More detailed validations under various conditions are required in the future. References [1] R. Kurose, H. Makino, Combust. Flame 135 (2003) 1–16. [2] R. Kurose, H. Watanabe, H. Makino, KONA Power Part. J. 27 (2009) 144–156. [3] K. Yamamoto, T. Murota, T. Okazaki, M. Taniguchi, Proc. Combust. Inst. 33 (2011) 1771–1778. [4] N. Hashimoto, R. Kurose, S.-M. Hwang, H. Tsuji, H. Shirai, Combust. Flame 159 (2012) 353–366. [5] O.T. Stein, G. Olenik, A. Kronenburg, et al., Flow Turbul. Combust 90 (2013) 859–884. [6] K. Yamamoto, D. Kina, T. Okazaki, M. Taniguchi, H. Okazaki, K. Ochi, in: ASME 2011 Power Conference, POWER2011-55367, 2011. [7] B.F. Magnussen, B.H. Hjertager, Proc. Combust. Inst. 16 (1977) 719–729. [8] N. Peters, Turbulent Combustion, Cambridge University Press, UK, 2000. [9] N. Peters, Proc. Combust. Inst. 21 (1986) 1231–1250. [10] C.D. Pierce, P. Moin, J. Fluid Mech. 504 (2004) 73–97. [11] H. Pitsch, M. Ihme, An unsteady/flamelet progress variable method for LES of nonpremixed turbulent combustion, AIAA Paper 2005-557, 2005. [12] M. Ihme, C.M. Cha, H. Pitsch, Proc. Combust. Inst. 30 (2005) 793–800. [13] K. Yunoki, T. Murota, K. Miura, T. Okazaki, in: ASME 2013 Power Conference, POWER2013-98143, 2013.
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Large-eddy simulation of pulverized coal combustion using flamelet model Junya Watanabe a,∗, Teruyuki Okazaki a, Kenji Yamamoto a, Koji Kuramashi b, Akira Baba b a Research
& Development Center, Mitsubishi Hitachi Power Systems, Ltd., 832-2 Horiguchi, Hitachinaka-shi, Ibaraki-ken 312-0034, Japan b Boiler Products Headquarters, Mitsubishi Hitachi Power Systems, Ltd., Japan Received 4 December 2015; accepted 5 June 2016 Available online xxx
Abstract A flamelet model for pulverized coal combustion, which considers three mixture fractions for coal moisture, volatile matter and gasified char, has been coupled with a large-eddy simulation. Its prediction accuracy for ignition and extinction has been investigated in the configurations of a lab-scale coal jet flame and a large-scale test furnace with an actual coal burner. For the lab-scale coal jet flame, the profile of the ratio of coal burnt on the central axis of the coal jet was compared with the measurement. The profile by the flamelet model well agreed with the experimental data within the measurement error. For the large-scale test furnace with the actual burner, the prediction ability for the ignition limit in a decreasing coal feed rate was examined. The present simulation reproduced an unstable flame state occurring at a lower coal feed rate. The ignition stability index, which was evaluated from the flame images, was compared with the test result. The sharp decline of the ignition stability index near the ignition limit was well-captured by the present simulation. The prediction error for the coal feed rate at the ignition limit was estimated to be within 10%. © 2016 by The Combustion Institute. Published by Elsevier Inc. Keywords: Pulverized coal combustion; Flamelet model; Large-eddy simulation; Turbulent jet flame; Ignition
1. Introduction We have to improve the pulverized coal combustion technologies to attain highly-efficient combustion and lower NOx emission in coal-fired thermal power plants. To develop innovative combustion
∗
Corresponding author. E-mail address: [email protected] (J. Watanabe).
technologies, the combustion state inside a coalfired boiler must be understood in detail. However, the huge size of boiler restricts thorough combustion tests in a real-scale. Also, quantitative measurements of pulverized coal combustion field are difficult. Numerical analysis is a powerful tool for a deep understanding of the phenomena and simulations of pulverized coal combustion have been extensively conducted. Recently, large-eddy simulation (LES) of pulverized coal combustion has been applied to laboratory-scale burners [1–5]. In our
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group, LES was also applied to a large-scale boiler furnace with a coal feed rate of 3000 kg/h [6]. The choice of turbulent combustion model affects the prediction accuracy of the simulation. In previous simulations of pulverized coal combustion, the eddy-breakup model and eddy dissipation model [7] have often been used because of their extensive application range. However, the concept of these models is intuitive as both unreasonably replace the chemical reaction time scale with a turbulent time scale [8]. These models also do not consider the flame structure that interacts with turbulence. Thus, these models cannot correctly reflect the influence of chemical kinetics and turbulence-chemistry interactions. In order to reproduce such non-equilibrium behavior as ignition and extinction, more sophisticated models that consider the finite rate chemistry with a detailed reaction mechanism are preferred. The high computational cost of such models for practical use is not affordable, however. The flamelet model is promising because it can take detailed chemical kinetics into account at a reasonable computational cost. Various flamelet models have been developed and applied to simulations of gaseous combustion [9–14] and spray combustion [15–17]. However, no flamelet model had been coupled with a coal combustion model that takes both devolatilization and the char surface reaction into account, although a flamelet model applied to gasified coal volatile combustion has been reported [18,19]. We proposed a new flamelet model concept applicable to the simulation of pulverized coal combustion in our previous study [20]. In the present study, the flamelet model is coupled with the LES to simulate a real combustor. The objective is to accurately reproduce the ignition of a pulverized coal burner, which is an important phenomenon for the combustor performance. The prediction accuracy for coal particle ignition and extinction is investigated in the configurations of a lab-scale coal jet flame and a large-scale test furnace with an actual burner.
Prandtl number is constant at 0.8. The radiation source term in the enthalpy equation is calculated by a discrete transfer radiation method [3,22]. The governing equations are solved by a finite volume method. The PISO approach [23] is employed to solve pressure–velocity coupling. The time step is determined so that the maximum Courant number is less than 0.2. A second order central difference scheme is used to calculate the convection terms. The minmod limiter function is applied for scalar equations. The diffusion term is evaluated by a second order central difference scheme. The mass, momentum and energy equations for coal particles are the same as those in [3] except that the moisture in coal particles is taken into account in the mass conservation equation.
2. Numerical methods
where ρ is the gas density, ui is the gas velocity, α is the thermal diffusivity, α sgs is the SGS thermal diffusivity, mmoi is the mass of moisture in a coal particle, mvol is the mass of volatile matter, mchar is the mass of char, and Vcell is the volume of a mesh cell. Overbar and tilde signs denote the spatial averaging and Favre averaging, respectively. The particlein-cell model [24] is used to calculate the last terms in Eqs. (1)–(3) [6]. The Lewis number is assumed to be unity. Here, Zmoi , Zvol and Zchar are defined as:
2.1. Governing equations The gas phase and coal particles are solved in an Eulerian manner and a Lagrangian manner, respectively. The Favre-filtered conservation equations for mass, momentum, enthalpy, and the state equation for ideal gas are solved in the gas phase. The source terms due to coal combustion are taken into account for the mass, momentum, and enthalpy conservation equations [3]. The subgrid-scale (SGS) stress tensor in the momentum equation is calculated by the Smagorinsky model [21]. The SGS thermal diffusivity in the enthalpy equation is calculated by assuming that the SGS turbulent
2.2. Flamelet model for coal combustion We extend the flamelet model for coal combustion developed in our previous study [20] to consider the moisture in a coal particle. In this model, the following Favre-filtered transport equations are solved: ∂ ρ¯ Z˜ moi ∂ ρ¯ u˜i Z˜ moi ∂ ∂ Z˜ moi + = ρ( ¯ α + α sgs ) ∂t ∂ xi ∂ xi ∂ xi 1 dmmoi − , Vcell parcel dt ∂ ρ¯ Z˜ vol ∂ ρ¯ u˜i Z˜ vol ∂ ∂ Z˜ vol + = ρ( ¯ α + α sgs ) ∂t ∂ xi ∂ xi ∂ xi 1 dmvol − , Vcell parcel dt ∂ ρ¯ Z˜ char ∂ ρ¯ u˜i Z˜ char ∂ ∂ Z˜ char + = ρ( ¯ α + α sgs ) ∂t ∂ xi ∂ xi ∂ xi 1 dmchar − , Vcell parcel dt
Z˜ moi = Z˜ vol =
Please cite this article as: J. Watanabe et al., coal combustion using flamelet model, Proceedings http://dx.doi.org/10.1016/j.proci.2016.06.031
(1)
(2)
(3)
m moi , m moi + m vol + m char + m ox
(4)
m vol , vol + m char + m ox
(5)
m
moi
+
m
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Z˜ char
m char = m moi + m vol + m char + m ox
where mmoi
(6)
evaporating moisture, mvol
is the mass of is the mass of gas originating from the volatile matter, mchar is the mass of gas originating from the char and mox is the mass of gas originating from the oxidant. The present model is based on the flamelet/progress variable (FPV) approach [10]. The following conservation equation of the progress variable Cpv is solved: ∂ C˜ pv ∂ ρ¯C˜ pv ∂ ρ¯ u˜iC˜ pv ∂ + = ρ¯ α + αsgs + S¯C pv ∂t ∂ xi ∂ xi ∂ xi (7) where SCpv is the source term of Cpv . In this study, we use the CO2 mass fraction as the progress variable (Cpv = YCO2 ). 2.3. Flamelet database The database of the species compositions are obtained by solving the flamelet equations. To avoid solving multi-dimensional flamelet equations [25,26], we introduce the following variables: Z˜ = Z˜ vol + Z˜ char + Z˜ moi
Table 1 Coal properties. Proximate analysis (dry basis wt%) Volatile matter Char Ash Fuel composition originating from the volatile matter, Yvol,k × 100 (wt%) CO CH4 C2 H2
Z˜ char m char = , m vol Z˜ vol
(9)
B=
Z˜ vol m vol = . m moi Z˜ moi
(10)
Ordinary one-dimensional flamelet equations with a single scalar dissipation rate χ are solved in Z space at different values of A and B. Depending on the values of A and B, the fuel composition of the flamelet equations changes. The details for determining the fuel composition are described in [20]. The fuel composition is determined as m moi Ymoi,k + m vol Yvol,k + (m char + m ox,conv )Ychar,k m moi + m vol + m char + m ox,conv MO2 +υMN2 1 A Ychar,k B Ymoi,k + Yvol,k + A + 0.5 MC = , (11) MO2 +υMN2 1 A B + 1 + A + 0.5 M
Y f uel,k =
C
where Ymoi,k is the composition of moisture, Yvol,k is the composition of gasified volatile matter, Ychar,k is the composition of gas produced through the char surface reaction, and mox,conv is the mass of oxidant consumed by the following char oxidation reaction: C + 0.5(O2 + υN2 ) → CO + 0.5υN2 .
(12)
MO2 , MN2 and MC denote the molecular weights of O2 , N2 and C, respectively. For the air oxidant, υ
31.1 54.0 14.9 34.8 24.5 40.7
is 3.76. Thus, CO and N2 are contained in the fuel gas from the char. Figure 1 shows the change of fuel composition Yfuel,k as a function of A and B for a bituminous coal having the properties listed in Table 1. The change of fuel composition is large for A < 1 and B < 4. Sufficient numbers of data points should be obtained in these ranges. The upper bound of Z in the flamelet equations, where the fuel composition is imposed, is calculated as Zmax = =
(8)
A=
3
m moi + m vol + m char m moi + m vol + m char + m ox,conv 1 B
1 B
+1+A
+υMN2 + 1 + A + 0.5 MO2M A
.
(13)
C
Also, the temperature assigned for the fuel gas is calculated by considering the temperature increase due to the heat of reaction of Eq. (12). The temperature increase is estimated by T =
Qox A +υMN2 Cp, f uel 1 + A + 0.5 MO2M A
(14)
C
where Qox is the heat of reaction of Eq. (12), and Cp,fuel is the specific heat of the fuel gas. Equation (14) assumes that all the heat released from the reaction (12) is transferred directly to the gas phase. Note that the fuel temperature estimated by using Eq. (14) gives only a reference value. In the present model, the flamelet database is generated at various temperatures decreasing from the reference temperature. This procedure makes it possible to consider the heat loss effect caused by radiation and the heat transfer to the solid phase in the flamelet database. The flamelet database is generated by FlameMaster [27] which solves the steady onedimensional flamelet equations at p = 0.1 MPa without radiation heat loss. The GRI-Mech 3.0 [28] is used as the reaction mechanism. Figure 2 shows the temperature profiles as a function of mixture fraction for different values of A and B. The profiles are for different levels of the progress variable. For B = 0.0, there is no temperature increase because only moisture is contained as the fuel gas. The peak temperature increases at higher
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Mass fraction of fuel Yfuel,k
4
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(a) B = 4.0 CH4 CO H2O
1 0.8
C2H2 N2
0.6 0.4 0.2
0 0
1
2
3
4
5
Mass fraction of fuel Yfuel,k
A 1
(b) A = 0.5
CH4 CO H2O
0.8
C2H2 N2
0.6 0.4 0.2 0 0
2
4
6
8
10
B Fig. 1. Fuel composition in flamelet equations as a function of (a) A at B = 4.0, and (b) B at A = 0.5.
Fig. 2. Temperature profiles as a function of Z for different A and B values. Arrows pointing to increasing Cpv are shown in each graph.
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5
Fig. 3. Instantaneous gas temperature distributions in the center plane.
B because less moisture is contained in the fuel gas at higher B. Also, the peak temperature increases at higher A, in which the char combustion progresses. Zmax becomes lower at higher A and B. The enthalpy h, which is obtained from the energy conservation equation including the heat source terms due to radiation and coal combustion, is also used as a reference parameter to take the effect of heat loss into account. As described above, the flamelet data are calculated at various fuel and oxidant temperatures to reproduce various enthalpy states. The fuel composition is determined from the flamelet data with the corresponding enthalpy value. In the present simulation, we couple the flamelet model with the LES. To take the SGS turbulence/chemistry interaction into account, a presumed probability density function (PDF) approach is introduced, in which the filtered quantities are written as ϕ˜ =
Zmax
ϕ (Z )P (Z )dZ.
(15)
0
A beta-PDF [1,29] is used to model the mixture fraction distribution. Consequently, the gas composition is determined from the flamelet database as Y˜ k = Yk Z˜ , Z˜ 2 , C˜ pv , A, B, h˜ . (16) In the present case, the flamelet data points are 100 × 20 × 30 × 5 × 5 × 7 for Z˜ × Z˜ 2 × C˜ pv × A × B × h˜ . The memory size for this database is approximately 1.5GB.
Table 2 Inlet conditions for lab-scale coal jet flame.
Zmoi Zvol Zchar Cpv
Primary jet
Preheated gas
Side boundary
0.01 0.0 0.0 0.0
0.082 0.041 0.0 0.133
0.0 0.0 0.0 0.0
3. Application to a lab-scale coal jet flame 3.1. Numerical conditions First, we apply the present simulation to a labscale ignition experiment, which has the same configuration and conditions as in our previous work [3] and details are given there. The mixture of pulverized coal and air is injected through the center nozzle and ignited by the co-flowing preheated gas. The diameter of the center nozzle is 7 mm. The injection velocity of primary jet is 10 m/s and the velocity of preheated gas is 4.8 m/s. The temperature of the preheated gas is 1510 K. The Reynolds number of the primary jet is about 4500. The case simulated here has the inlet stoichiometric ratio of 0.22. The inlet boundary conditions for the flamelet simulation are listed in Table 2. 3.2. Numerical simulation results Figure 3 shows instantaneous gas temperature distributions in the center plane. The flamelet model results are plotted in Fig. 3(a) and previous results [3] obtained by an eddy-dissipation concept (EDC) model are shown in Fig. 3(b). Qualitatively
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points. It is implied that the flamelet model captures the jet core temperature (shown in Fig. 3) more accurately than the EDC model.
60 Flamelet model EDC model [8] Exp.
50 40 30
4. Application to a large-scale test furnace with an actual pulverized coal burner
20 10
4.1. Experimental and numerical conditions
0 0
100
200 300 400 Axial position, mm
500
Fig. 4. Comparison of the ratio of coal burnt on the centerline.
similar turbulent combustion fields can be observed for both simulations. The turbulent mixing layer develops between the primary jet and the preheated co-flow. A lifted flame is formed there. The flame temperature is almost the same for both simulations, although the relatively low-temperature jet core remains more downstream in the EDC model. Figure 4 compares the distribution of the ratio of coal burnt on the centerline. The simulation results by the flamelet model and the EDC model [3] are compared with the experimental data by the probe sampling [30]. Overall, good agreement with the experiment is obtained for both simulations. In the EDC model, the ratio of coal burnt is underestimated at the position 300 mm downstream from the nozzle exit. On the other hand, in the flamelet model, the ratio of coal burnt starts to increase earlier than in the EDC model and its distribution is within the measurement error at all measurement
Our second application is for a low-load testing of the HT-NR3 burner [31] in a large-scale test rig. Figure 5 shows the computational mesh of the test rig. A single burner is attached on the furnace. The mesh has approximately 840,000 cells and is refined only near the burner because we focus on the ignition state that occurs in the burner zone. The diameter of the primary nozzle exit is 447 mm. To investigate the ignition limit of the burner, the mass flow rate of coal is decreased from a stably combusting state under a constant air flow rate condition. The mass flow rates are 2.62 kg/s for the burner air and 0.56 kg/s for the additional air, respectively. The boundary conditions for Zmoi , Zvol , Zchar and Cpv are fixed to be zero at all inlet boundaries. 4.2. Results of combustion test Figure 6 shows images of the flame taken near the burner in a decreasing coal feed rate. Four arbitrary instants are selected for the images to observe the unsteady behavior. The flame stabilizing ring (FSR) attached at the primary nozzle exit is drawn as a solid line in the images. In all cases, a luminous flame is formed from the FSR. The luminous flame occasionally disappears for a part of
Outlet Additional air ports
Secondary air Primary nozzle
Coal + Primary air
Secondary air
HT-NR3 burner
Furnace
Fig. 5. Computational mesh for large-scale test furnace.
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Coal feed rate
Low
7
High
FSR No.1 A
A No.2
A No.3 A
A No.4 A
Fig. 6. Flame images in the combustion test.
a E D C
FSR A B
Gas temperature [K] 350 1900
b Recirculation region
Ignition region
Unburnt region
Fig. 7. Simulated instantaneous gas temperature distribution (a) in the vertical plane through the center of the burner and (b) on the dashed line “E”.
FSR at lower coal feed rates, as shown by “A” in the images. At the lowest coal feed rate in the test, the flame is highly unstable because partial disappearance of the luminous flame frequently occurs. The coal feed rate decrease is stopped here to avoid the flame extinction. 4.3. Numerical results Figure 7(a) shows the instantaneous gas temperature distribution in the vertical plane through
the center of the burner under a stably combusting state. The primary air with pulverized coal flows straightly (arrow “A”) and the secondary air flows outwardly (arrow “B”). These two flows generate a large recirculation flow (arrow “C”) behind the FSR. A part of the hot burnt gas is entrained by this recirculation flow, enhancing the ignition of pulverized coal near the FSR. The gas temperature rapidly increases just behind the FSR and the stable flame develops downstream (region “D”). Figure 7(b) shows the gas temperature profile on
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Coal feed rate
Low
High
Fig. 8. Simulated isosurfaces of 1400 K in a decreasing coal feed rate.
Fig. 9. Examples to evaluate the ignition stability index. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)
the dashed line “E” shown in Fig. 7(a). The temperature of burnt gas in the recirculation zone is roughly 1260 K. The temperature rapidly increases between the unburnt primary air and the recirculation zone. The coal particles are heated and ignition occurs in this region. The coal jet flame ignited by the burnt gas can be detected by temperature isosurfaces of 1400 K, which is about 10% higher than that of the burnt gas. Figure 8 shows instantaneous isosurfaces of 1400 K. An arbitrary instant is shown. A highly turbulent flame can be observed. At higher coal feed rates, the flame is formed on the entire circumference of the FSR. At the second lowest coal feed rate, the flame region decreases remarkably and it is formed on only a part of the FSR. At the lowest coal feed rate, only a small flame can be observed.
to d is calculated for each image, averaging for Ns -number of images. Figure 10 compares the ignition stability index for lowering coal feed rates between the experiment and the simulation. The coal feed rates are normalized by the value in the stably combusting state. The flame stability index rapidly decreases below the normalized coal feed rate of 0.6 in the combustion experiment. This trend is well reproduced by the present simulation, although the numerical value is slightly lower than the experimental one. When the ignition stability index at the lowest coal feed rate in the experiment is used as a criterion, the error of the coal feed rate at the ignition limit is 9.6% in the present simulation. Thus, the present simulation predicts the ignition limit with less than 10% error.
4.4. Comparison of ignition stability 5. Conclusions To evaluate the ignition stability from the flame images shown in Figs. 6 and 8, we define the following index: Ignition stability index (%) =
Ns 1 l · 100. (17) Ns i=1 d
Figure 9 shows examples to evaluate the ignition stability index. Here, d is the length of the primary nozzle diameter in the flame image. The vertical line with a length of d (shown as a dashed line) is put at the position of d apart from the nozzle exit. Then, the luminous flame area on the vertical line (marked by the short red lines) is manually detected and its length is l. The percentage of l
The LES coupled with the newly-developed flamelet model for pulverized coal combustion was demonstrated in two configurations of a lab-scale coal jet flame and a large-scale combustion test of an actual pulverized coal burner. For the lab-scale coal jet flame, the profile of the ratio of coal burnt obtained by the present flamelet model was compared with the experiment and our previous simulation using an EDC model. The prediction accuracy of the ratio of coal burnt near the ignition point was improved compared to the EDC model. The profile of the ratio of coal burnt obtained by the present simulation was within the measurement error on the central axis.
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9
100 80 Experiment Simulation
60
40 20
Error 9.6%
0 0
0.2 0.4 0.6 0.8 1 1.2 Normalized coal feed rate (arb. unit)
Fig. 10. Comparison of ignition stability index.
For the large-scale combustion test of an actual pulverized coal burner, where the coal feed rate was lowered from a stably combusting state, the present simulation reproduced the unstable flame observed in the test near the ignition limit. The prediction error for the coal feed rate at the ignition limit was estimated to be within 10% in the present case. More detailed validations under various conditions are required in the future. References [1] R. Kurose, H. Makino, Combust. Flame 135 (2003) 1–16. [2] R. Kurose, H. Watanabe, H. Makino, KONA Power Part. J. 27 (2009) 144–156. [3] K. Yamamoto, T. Murota, T. Okazaki, M. Taniguchi, Proc. Combust. Inst. 33 (2011) 1771–1778. [4] N. Hashimoto, R. Kurose, S.-M. Hwang, H. Tsuji, H. Shirai, Combust. Flame 159 (2012) 353–366. [5] O.T. Stein, G. Olenik, A. Kronenburg, et al., Flow Turbul. Combust 90 (2013) 859–884. [6] K. Yamamoto, D. Kina, T. Okazaki, M. Taniguchi, H. Okazaki, K. Ochi, in: ASME 2011 Power Conference, POWER2011-55367, 2011. [7] B.F. Magnussen, B.H. Hjertager, Proc. Combust. Inst. 16 (1977) 719–729. [8] N. Peters, Turbulent Combustion, Cambridge University Press, UK, 2000. [9] N. Peters, Proc. Combust. Inst. 21 (1986) 1231–1250. [10] C.D. Pierce, P. Moin, J. Fluid Mech. 504 (2004) 73–97. [11] H. Pitsch, M. Ihme, An unsteady/flamelet progress variable method for LES of nonpremixed turbulent combustion, AIAA Paper 2005-557, 2005. [12] M. Ihme, C.M. Cha, H. Pitsch, Proc. Combust. Inst. 30 (2005) 793–800. [13] K. Yunoki, T. Murota, K. Miura, T. Okazaki, in: ASME 2013 Power Conference, POWER2013-98143, 2013.
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